How do you solve Distribute Candies Among Children II on LeetCode?

Distribute Candies Among Children II (LeetCode #2929) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(1) time complexity and O(1) space complexity. Key insight: Understanding combinatorial counting can significantly reduce the complexity of distribution problems.

What is the time complexity of Distribute Candies Among Children II?

The optimal solution for Distribute Candies Among Children II runs in O(1) time and uses O(1) space. The time complexity is O(1) since we are using combinatorial calculations which do not depend on n in a linear or quadratic manner.

What is the brute force solution for Distribute Candies Among Children II?

The brute force approach for Distribute Candies Among Children II is Brute Force, with O(n²) time complexity and O(1) space complexity. We can try every possible distribution of candies among the three children. This involves iterating through all possible amounts for the first child, then for the second child, and calculating the third child based on the remaining candies. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve Distribute Candies Among Children II?

Distribute Candies Among Children II uses the following concepts: Math, Combinatorics, Enumeration. The recommended patterns to study are: Combinatorics, Inclusion-Exclusion Principle.

What are the interview tips for Distribute Candies Among Children II?

Always consider if there is a mathematical way to solve the problem before jumping into coding. Be clear about edge cases, especially when limits are involved. Practice explaining your thought process as you work through the problem.

What are common mistakes when solving Distribute Candies Among Children II?

Failing to account for the limits on the number of candies each child can receive. Not using combinatorial math effectively, leading to inefficient brute-force solutions.

#2929

Distribute Candies Among Children II

Medium

MathCombinatoricsEnumerationCombinatoricsInclusion-Exclusion Principle

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(1)
Space	O(1)	O(1)

💡

Intuition

Time O(1)Space O(1)

Instead of iterating through all combinations, we can use combinatorial math to determine the number of valid distributions directly. We can calculate how many ways we can distribute candies to the children while respecting the limit.

⚙️

Algorithm

4 steps

1Step 1: Calculate the maximum number of candies each child can receive, which is min(limit, n).
2Step 2: Use combinatorial counting to find the number of ways to distribute the remaining candies after assigning a certain amount to one child.
3Step 3: The formula to use is (n + 2) choose 2, which gives us the total combinations of distributing n candies to 3 children without any limit. We then subtract the invalid cases where any child exceeds the limit.
4Step 4: Use the principle of inclusion-exclusion to account for over-distributions.

solution.py6 lines

1from math import comb
2
3def distributeCandies(n, limit):
4    if n > 3 * limit:
5        return 0
6    return comb(n + 2, 2) - 3 * comb(n - limit - 1, 2) + 3 * comb(n - 2 * limit - 1, 2) if n - 2 * limit >= 0 else 0

ℹ

Complexity note: The time complexity is O(1) since we are using combinatorial calculations which do not depend on n in a linear or quadratic manner.

1Understanding combinatorial counting can significantly reduce the complexity of distribution problems.
2Using the principle of inclusion-exclusion helps in accurately counting valid distributions.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.